The twelve edge totals of a standard six-sided die are distributed symmetrically. Will the same symmetry emerge with a dodecahedral die?
Toni Beardon has chosen this article introducing a rich area for
practical exploration and discovery in 3D geometry
Glarsynost lives on a planet whose shape is that of a perfect
regular dodecahedron. Can you describe the shortest journey she can
make to ensure that she will see every part of the planet?
A description of how to make the five Platonic solids out of paper.
What are the shortest distances between the centres of opposite
faces of a regular solid dodecahedron on the surface and through
the middle of the dodecahedron?
What is the shortest distance through the middle of a dodecahedron between the centres of two opposite faces?
Follow instructions to fold sheets of A4 paper into pentagons and assemble them to form a dodecahedron. Calculate the error in the angle of the not perfectly regular pentagons you make.